It is therefore very important for the petroleum industry to identify, on the one hand, the damage type and, on the other hand, the damaged zones in order to optimize the acid stimulation parameters so as to produce wormholes with an optimum density and depth of penetration in the formation.
The formation and the behaviour of wormholes can be studied according to four different scales in order to determine the acid injection parameters:
the pore scale, which is the scale on which the chemical reaction mechanisms are described,
the core scale, on which the wormhole instability appears,
the well scale, which is the scale on which the competition between the wormholes and the impact of the heterogeneities on this scale can be appreciated,
the reservoir scale, on which the effect of stimulation is measured by the skin factor.
FIGS. 1A to 1D, where medium σ represents the rock and medium β the water and the acid, illustrate these different scales involved in the acid stimulation:
FIG. 1A: pore scale (μm-mm)
FIG. 1B: core scale (mm-cm)
FIG. 1C: well scale (cm-m)
FIG. 1D: reservoir scale (m-km).
Many models such as those shown by Wang, Y., Hill, A. D., and Schechter, R. S., “The Optimum Injection Rate for Matrix Acidizing of Carbonate Formations”, Paper SPE 26578, SPE ATCE, Houston, 1993, have already been proposed to study the effect of fluid leakage, of kinetic reactions, etc., on the rate of propagation of wormholes and the effect of the neighbouring wormholes on the dominant wormhole growth rate. The simple structure of these models has the advantage of studying in detail the reaction, the diffusion and convection mechanisms within the wormholes. However, these models cannot be used to study the initialization of wormholes and the effects on the formation heterogeneities.
Models describing dissolution upon acid injection have been used for the first time to describe this phenomenon on the scale of the pore. Such a method is for example described in Hoefner, M. L., Fogler, H. S., “Pore Evolution and Channel Formation During Flow and Reaction in Porous Media”, AIChE J, 34, 45-54 (1998). However, core-scale simulation from these models is difficult and requires a high calculating capacity. Now, it is on this scale that the instabilities due to wormholes appear.
The first core-scale model likely to totally reproduce the dissolution mechanisms was proposed by Golfier, F. et al., “A discussion on a Darcy-scale modelling of porous media dissolution in homogeneous systems”, Computational Methods in Water Resources, 2, 1195-1202 (2002). This single-medium model is constructed from a volume averaging of the equations on the scale of the pore. This modelling has also been used in international patent application WO-03/102,362, which has extended the model to the case of a dissolution limited by the reaction kinetics. These models are based on a core-scale physics description, which requires grid cell sizes of the order of one millimeter.
However, an acid injection process is a well-scale process. It is therefore necessary to model the formation and the behaviour of the wormholes on this scale, all the more so since, in the petroleum industry, the spread of horizontal wells has generated an increase in the amounts of acid injected in a single well. The simulation means needs for increasing the chances of success of the treatment have grown. Now, the modellings described above do not allow to simulate acidification over a range representing the section of a well and its surroundings (1 to 3 m).
Models intended to simulate acid treatment on a larger scale than the core scale have already been proposed. Examples thereof are:
Buisje, M. A. Understanding Wormholing Mechanisms Can Improve Acid Treatments in Carbonate Formations. (SPE 38166). 1997. SPE European Formation Damage Conference.
Buisje, M. A. & Glasbergen, G. (SPE 96892). 2005. SPE Annual Technical conference and Exhibition.
Gdanski, R. A Fundamentally New Model of Acid Wormholing in Carbonates. (SPE 54719). 1999. SPE European Formation Damage Conference.
These methods rest on empirical considerations based on laboratory observations that are very far from the real conditions and dimensions.
The method according to the invention is a method for metric-scale modelling of the acidification within a porous medium as a result of acid injection, allowing to meet reservoir engineers' requirements for defining a suitable acid well stimulation scenario within the context of carbonate reservoirs.